It came after the Supreme Court criticised the Government's €1.1m information campaign as unfair and unbalanced. It has been cited as a possible reason for the higher than expected 42pc No vote and the 33pc turnout.

Ms Burton said the Government would have to give careful consideration to setting up the independent Referendum Commission on a permanent footing, so that it could look after all the information for a referendum campaign.

Currently, the Referendum Commission is set up in the lead-up to each referendum and is traditionally headed by a High Court judge. It produced its own information booklet for the children's referendum.

Ms Burton also told RTE's Morning Ireland that she believed there should be research into the reasons for the size of the No vote in the children's referendum.

Meanwhile, Junior Minister Brian Hayes has blamed voter apathy and the lack of media coverage for the poor turnout.

The shocking turnout of only one in three voters was the third-lowest on a referendum polling day.

Mr Hayes said there was a lot of voter apathy, with many people in his Dublin South West constituency telling him they were not going to bother to turn out.

“There was an assumption that this was going to be carried in an easy way,” he said.

And Mr Hayes also said it had been difficult for broadcasters to organise as many debates on the children’s referendum as they had in the fiscal treaty referendum.

“You required a Yes and a No side to present themselves and given that the number of people against the referendum was quite small and they weren’t as organised, it was difficult for the media to present that,” he told RTE's Today with Pat Kenny Show.

Mr Hayes backed up Joan Burton by declaring that he also supported the concept of a permanent and expanded Referendum Commission to keep voters informed – rather than it being set up temporarily before every referendum.

However, Sinn Fein TD Caoimghin O’Caolain said his party was wary of this because it would cost considerably more to do – and the existing Referendum Commission had done a good job during the children’s referendum.